Electromagnetic filter device

ABSTRACT

The optical filter device comprises a stack of thin layers exhibiting a sequences h and g which defines a fractal organization. This device makes it possible to obtain spectrum lines which are extremely fine and very well resolved.

This is a continuation of application No. 07/327,052 filed Nov. 22, 1989now abandoned.

The present invention relates to an electromagnetic filter device.

In the field of lightwaves, prior art optical filter devices areinterference filters based on the principle of stacking up thin layers,which can be made, in particular, by modern vacuum evaporationtechniques. The thin layers may be made of metal material or ofdielectric material and the thicknesses thereof may lie in a wide rangeof values, running from a few nanometers to several microns.

It is currently possible to make very narrow band filters, e.g.Fabry-Perot filters, capable of selecting spectrum lines having a widthof as little as a few nanometers, together with harmonics thereof. Suchfilters comprise at least a score of λ/4 layers together with λ/2Fabry-Perot cavities in series.

It is also possible to make filters capable of having identicaltransmission for two predetermined spectrum lines which are notharmonics of each other, but there is no known simple method of goingbeyond that.

It is also common practice to make highpass filters and lowpass filters.With more difficulty, it is possible to make bandpass filters and to usethem as "subtraction-filters" which are more complex and which eliminatea band from within a determined spectrum range. It is not known how tomake a filter having several pass bands.

At oblique angles of incidence, it is also possible to change therectilinear, circular, or elliptical vibration of a light beam by usingphase-shifting coatings, and even to physically separate twoperpendicular directions of vibration by using polarizing coatings as isdone, for example, in MacNeille polarizing cubes.

The object of the present invention is to provide a filter devicesuitable for providing an extremely narrow transmission spectrum linewithout any emission in its immediate vicinity, i.e. a line which iswell isolated in the spectrum, or for providing a plurality of spectrumlines which are not harmonics of one another, or for providing aplurality of bands which are not harmonics of one another.

The present invention provides an electromagnetic filter devicecomprising a stack of electromagnetic cavities in the form of layers,the device being characterized by the fact that a first cavity of layerA of natural frequency w₀ and a second cavity of layer B of naturalfrequency w₁ are used, and the stack of layers A_(n), FIG. 10, where nis greater than 1, has sequences h and g sequence f such that: ##EQU1##

said stack thus exhibiting fractal organization.

By way of example, the following A_(n) stacks may be obtained:

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1

with

    B.sub.n =B.sub.n-1 B.sub.n-1 B.sub.n-1, A.sub.1 =ABA and B.sub.1 =BBB

or

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1

with

    B.sub.n =A.sub.n-1 A.sub.n-1 A.sub.n-1, A.sub.1 =ABA and B.sub.1 =AAA

or

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1 B.sub.n-1 A.sub.n-1

with

    B.sub.n =B.sub.n-1 B.sub.n-1 B.sub.n-1 B.sub.n-1 B.sub.n-1, A.sub.1 =ABABA, B.sub.1 =BBBBB

or

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1 B.sub.n-1 A.sub.n-1

with

    B.sub.n =A.sub.n-1 A.sub.n-1 A.sub.n-1 A.sub.n-1 A.sub.n-1 =ABABA, B.sub.1 =AAAAA

or

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1 B.sub.n-1

with

    B.sub.n =B.sub.n-1 B.sub.n-1 B.sub.n-1 B.sub.n-1, A.sub.1 =ABAB, B.sub.1 =BBBB

or

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1 B.sub.n-1

with

    B.sub.n =A.sub.n-1 A.sub.n-1 A.sub.n-1 A.sub.n-1, A.sub.1 =ABAB, B.sub.1 =AAAA

or

    A.sub.n =A.sub.n-a A.sub.n-1 B.sub.n-1 B.sub.n-1

with

    B.sub.n =B.sub.n-1 B.sub.n-1 B.sub.n-1 B.sub.n-1, A.sub.1 =AABB and B.sub.1 =BBBB

or

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1 B.sub.n-1

with

    B.sub.n =A.sub.n-1 A.sub.n-1 A.sub.n-1 A.sub.n-1, A.sub.1 =ABAB, B.sub.1 =AAAA

or

    A.sub.n =A.sub.n-1 A.sub.n-1 B.sub.n-1 B.sub.n-1

with

    B.sub.n =B.sub.n-1 B.sub.n-1 B.sub.n-1 B.sub.n-1, A.sub.1 =AABB and B.sub.1 =BBBB or

    A.sub.n =A.sub.n-1 A.sub.n-1 B.sub.n-1 B.sub.n-1 with

    B.sub.n =A.sub.n-1 A.sub.n-1 A.sub.n-1 A.sub.n-1, A.sub.1 =AABB and B.sub.1 =AAAA

The values of the natural frequencies w₀ and w₁ are defined by thethicknesses e_(A) and e_(B) and the refractive indices n_(A) and n_(B)of the corresponding cavities of layers A and B.

The first stack of the invention is a stack of order 2.

Thus, for a device having a stack or order 2, the following successionof filters may be used, for example:

A₂ =A₁ B₁ A₁ =ABABBBABA, corresponding to seven superposed layers.

B₂ =BBBBBBBBB, formed of succeeding same layers.

For a device having a stack of order 3, the following succession offilters may be used:

A₃ =A₂ B₂ A₂ =ABABBBABABBBBBBBBBABABBBABA (with 15 layers)

B₃ =B₂ B₂ B₂ =BBBBBBBBBBBBBBBBBBBBBBBBBBB (with succeeding same layers).

The filters A₂, A₃, and A_(n) constitute examples of fractally-organizedstacks.

Other characteristics and advantages of the present invention appearfrom the following description of embodiments given by way ofnon-limiting example.

FIG. 1 shows variation in the energy T transmitted by a prior art ABAtype filter as a function of the normalized frequency f of the incidentbeam.

FIGS. 2, 3, and 4 are views analogous to FIG. 1 but applicable todifferent filters of the invention, being respectively of order 2, 3,and 4.

FIG. 5 is a view analogous to FIG. 1 for a prior art filter of the ABABAtype.

FIG. 6 is a view analogous to FIG. 2 for a filter of the invention oforder 2, but having the following stack ABABABBBBBABABABBBBBABABA.

FIG. 7 is analogous to FIG. 6 for an order 3 filter of the invention.

FIGS. 8A and 8B are analogous to FIG. 7 for an order 4 filter of theinvention.

FIG. 9 is a "strange attractor" diagram showing variation in frequencytransmission as a function of variation in the refractive index of Brelative to the refractive index of A for an ABABBBABA filter.

FIG. 10 is a schematic elevational view of a filter structure of genericform covering the embodiments of the invention illustrated in FIGS. 1-9.

We begin with a filter layer A having a refractive index n_(A) =2.4 anda filter layer B having a refractive index n_(B) =1.35.

The thicknesses of A and B are selected in such a manner that w₀ =w₁. Aprior art filter stack A₁ =ABA is made whose total optical thickness isequal to 10 microns. The frequencies f are normalized by the factor3×10⁸. It can be seen in FIG. 1 that the passband on the fundamentalenergy, i.e. excluding harmonics, lies between f₁ and f₂, and undesiredperiodicity in the spectrum can be seen. Resolution is very mediocre andisolated bands cannot be seen.

FIG. 2 corresponds to transmission through an order 2 filter, i.e.corresponding to an ABABBBABA stack of the invention having a totaloptical thickness equal to 10 microns. The thickness of the filter layerA is then e₁ =0.469 μm and the thickness of the filter layer B is e_(B)=0.823 μm. Fine spectrum lines f₃ and f₄ of width 1600 Å and which arevery well resolved appear on the edges.

FIG. 3 corresponds to transmission through an order 3 filter, i.e.corresponding to an ABABBABABBBBBBBBBABABBBABA stack having a totaloptical thickness equal to 10 microns. The thickness of filter layer Ais e_(A) =0.154 μm and the thickness of the filter layer B is e_(B)=0.274 μm. The spectrum lines are finer, and in particular, two spectrumlines f₅ and f₆ can be observed which are thoroughly independent of eachother, with f₆ being particularly well resolved. The width of this lineis 53 Å. A very well resolved passband between f₇ and f₈ can also beseen to appear.

The result is even more significant in FIG. 4 which shows thetransmission of an order 4 filter for which e_(A) =514 Å and e_(B) =914Å. Very well isolated spectrum lines occur at frequencies f₉, f₁₀, andf₁₁, each having a width of much less than 10 Å.

A filter device is then shown comprising another ABABA type of prior artstack. We still begin with a filter layer A of refractive index 2.4 anda filter layer B of refractive index 1.35. The total optical thicknessof the filter is 10 microns, with the thickness of filter layer A being1.64 μ and the thickness of filter layer B being 2.537 μ.

FIG. 5 shows the transmission of this filter which had poor resolution.

FIG. 6 corresponds to an order 2 filter of the invention, i.e. a filterhaving the stack; ABABABBBBBABABABBBBBABABA over an optical thickness of10 microns. The thickness of the layer A is 0.269 μ and that of thelayer B is 0.416 μ. Good passbands can be seen to appear together withisolated spectrum lines at frequencies f₁₂ and f₁₃ which are notharmonics of each other.

FIG. 7 corresponds to a filter having the same sequence as that of FIG.6 but or order 3. The thickness of layer A is then 440 Å and thethickness of layer B is 1060 Å. Very fine spectrum lines now appear atthe edges of the spectrum at frequencies f₁₄ and f₁₅. These lines arevery well resolved. Well separated passbands also appear.

This phenomenon can also be seen in FIGS. 8A and 8B which relate to afilter having the same sequence, but of order 4. In this case, thethickness of layer A is 100 Å and the thickness of layer B is 110 Å.Spectrum lines can be observed at f₁₄, f₁₅, and f₁₆.

FIG. 9 shows how the transmitted frequencies vary as a function ofchange in the ratio between the refractive indices of A and B. Thediagram obtained is a strange attractor. This variant corresponds to afilter of order 2 as shown in FIG. 2, with a layer A of refractive indexequal to 2.4 and a layer B of refractive index varying (along the Xaxis) from 1.2 to 9.

When the transmittance is greater than 0.7 a black point is marked, andwhen the transmittance is less, a white point is marked. It can be seenthat frequency selection is easier in some index zones. Knowledge of thestrange attractor makes it possible to establish relative values ofindices suitable for locating a selected band.

Naturally, the invention is not limited to the embodiments describedabove, in particular the invention is not limited to filtering opticalwavelengths. Further, the sequence can be applied either to thegeometrical thicknesses of the layers or else to the optical thicknessesof the layers.

Finally, the thicknesses of the layers of a build-up assembly of order ncan be changed by compression or rolling, etc.

We claim:
 1. Electromagnetic filtering device comprising a stack A_(n),wherein n is greater than or equal to 2, said stack consisting of layersA and B having the thicknesses e_(A) and e_(B) respectively, and therefractive indices n_(A) and n_(B) respectively, and wherein said stackA_(n) has the following fractal configuration:

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1

where B_(n) =B_(n-1) B_(n-1) B_(n-1), A₁ =ABA and B₁ =BBB. 2.Electromagnetic filtering device comprising a stack A_(n), wherein n isgreater than or equal to 2, said stack consisting of layers A and Bhaving the thicknesses e_(A) and e_(B) respectively, and the refractiveindices n_(A) and n_(B) respectively, and wherein said stack A_(n) hasthe following fractal configuration:

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1

where

    B.sub.n =A.sub.n-1 A.sub.n-1 A.sub.n-1, A.sub.1 =ABA and B.sub.1 =AAA.


3. Electromagnetic filtering device comprising a stack A_(n), wherein nis greater than or equal to 2, said stack consisting of layers A and Bhaving the thicknesses e_(A) and e_(B) respectively, and the refractiveindices n_(A) and n_(B) respectively, and wherein said stack A_(n) hasthe following fractal configuration:

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1 B.sub.n-1 A.sub.n-1

where

    B.sub.n =B.sub.n-1 B.sub.n-1 B.sub.n-1 B.sub.n-1 B.sub.n-1, A.sub.1 =ABABA, B.sub.1 =BBBBB.


4. Electromagnetic filtering device comprising a stack A_(n), wherein nis greater than or equal to 2, said stack consisting of layers A and Bhaving the thicknesses e_(A) and e_(B) respectively, and the refractiveindices n_(A) and n_(B) respectively, and wherein said stack A_(n) hasthe following fractal configuration:

    A.sub.n +A.sub.n-1 B.sub.n-1 A.sub.n-1 B.sub.n-1 A.sub.n-1

wherein

    B.sub.n =A.sub.n-1 A.sub.n-1 A.sub.n-1 A.sub.n-1 A.sub.n-1, A.sub.1 =ABABA, B.sub.1 =AAAAA.


5. Electromagnetic filtering device comprising a stack A_(n), wherein nis greater than or equal to 2, said stack consisting of layers A and Bhaving the thicknesses e_(A) and e_(B) respectively, and the refractiveindices n_(A) and n_(B) respectively, and wherein said stack A_(n) hasthe following fractal configuration:

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1 B.sub.n-1

where

    B.sub.n =B.sub.n-1 B.sub.n-1 B.sub.n-1 B.sub.n-1, A.sub.1 =ABAB, B.sub.1 =BBBB.


6. Electromagnetic filtering device comprising a stack A_(n), wherein nis greater than or equal to 2, said stack consisting of layers A and Bhaving the thicknesses e_(A) and e_(B) respectively, and the refractiveindices n_(A) and n_(B) respectively, and wherein said stack A_(n) hasthe following fractal configuration:

    A.sub.n =A.sub.n-1 B.sub.n-1 A.sub.n-1 B.sub.n-1

where

    B.sub.n =A.sub.n-1 A.sub.n-1 A.sub.n-1 A.sub.n-1, A.sub.1 =ABAB, B.sub.1 =AAAA.


7. Electromagnetic filtering device comprising a stack A_(n), wherein nis greater than or equal to 2, said stack consisting of layers A and Bhaving the thicknesses e_(A) and e_(B) respectively, and the refractiveindices n_(A) and n_(B) respectively, and wherein said stack A_(n) hasthe following fractal configuration:

    A.sub.n =A.sub.n-1 A.sub.n-1 B.sub.n-1 B.sub.n-1

where

    B.sub.n =B.sub.n-1 B.sub.n-1 B.sub.n-1 B.sub.n-1, A.sub.1 =AABB, B.sub.1 =BBBB.


8. Electromagnetic filtering device comprising a stack A_(n), wherein nis greater than or equal to 2, said stack consisting of layers A and Bhaving the thicknesses e_(A) and e_(B) respectively, and the refractiveindices n_(A) and n_(B) respectively, and wherein said stack A_(n) hasthe following fractal configuration:

    A.sub.n =A.sub.n-1 A.sub.n-1 B.sub.n-1 B.sub.n-1

where

    B.sub.n =A.sub.n-1 A.sub.n-1 A.sub.n-1 A.sub.n-1, A.sub.1 =AABB, B.sub.1 =AAAA.